Surface density of charge on a charged conducting sphere of radius 'R' in terms of electric intensity 'E' at…

Surface density of charge on a charged conducting sphere of radius 'R' in terms of electric intensity 'E' at a distance 'r' in free space is $\left(\mathrm{r}>\mathrm{R}, \mathrm{E}_{0}=\right.$ permittivity of free space $)$
  1. \(E \in 0 \left(\frac{R}{r}\right)\)
  2. \(E \in 0 \left(\frac{r}{R}\right)^{2}\)
  3. \(E \in 0 \left(\frac{r}{R}\right)\)
  4. \(E \in 0 \left(\frac{R}{r}\right)^{2}\)

Solution

$E=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{r^{2}}=\frac{1}{4 \pi \varepsilon_{0}} \frac{4 \pi R^{2} \sigma}{r^{2}}=\frac{\sigma R^{2}}{\varepsilon_{0} r^{2}}$ $\therefore \sigma=E \varepsilon_{0}\left(\frac{r}{R}\right)^{2}$

Asked in: MHT CET 2020 (16 Oct Shift 1)

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